Spatial Linear Instability of Confluent Wake/Boundary Layers

Aerofoil wake-induced transition characteristics on a flat-plate boundary layer

“…In the present experiment (for , 60 and 80 mm), the aerofoil was positioned at for all streamwise stations, which is significantly higher than this threshold. Therefore, the similar growth rate for the , 60 and 80 mm base flow velocity profiles is consistent with the findings of Liou & Liu (2001).…”

“…It is worth mentioning that the growth rates of the boundary layer mode shown in figure 16( a ) were found to be same for the and 80 mm base flow velocity profiles, and it is understood from Liou & Liu (2001) that, above a certain (), the boundary layer mode is unaffected, i.e. eigenvalues remains constant.…”

“…To compute the unstable modes, the algorithm of Haj-Hariri (1988), Varghese (2016) and Mitra (2018) was employed with a Chebyshev spectral method (Schmid & Henningson 2012) for discretising the equation in the wall-normal direction. The method was validated with the more relevant study conducted by Liou & Liu (2001), see Appendix A. To obtain a smooth base flow profile without any discontinuities in the derivatives, a confluent wake–boundary layer profile is generated numerically to match the measured wake profile.…”

“…By rearranging (A1), the Orr–Sommerfeld equation can be cast as an eigenvalue problem (A2), particularly for the present study (wake–boundary layer) considered as a spatial eigenvalue problem. Upon imposing the boundary conditions ( at the solid wall and far field) it is solved for complex wavenumber (), by considering to be real The method used for the present analysis has been validated with a rather relevant analysis conducted by Liou & Liu (2001) on the confluent wake–boundary layer. Following their approach, a base flow velocity profile is modelled by superposition of the Blasius boundary layer profile and the Gaussian wake profile (), shown in figure 22( a ).…”

“…Following their approach, a base flow velocity profile is modelled by superposition of the Blasius boundary layer profile and the Gaussian wake profile (), shown in figure 22( a ). By considering the same geometry of the wake, and as reported in Liou & Liu (2001), the Orr–Sommerfeld equation is solved using the approach indicated earlier and three discrete unstable modes are obtained: one boundary layer mode and two wake modes (shown in figure 22 b ). The wake modes 1 and 2 correspond to antisymmetric and symmetric modes, respectively.…”